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Understanding Rational Numbers: Decimals & Fractions Mastery

Enhance math skills by converting fractions to decimals, decimals to fractions, and solving real-world examples. Learn the steps and practical applications to master rational numbers. Prepare for multi-step problems with integers, percents, and more.

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Understanding Rational Numbers: Decimals & Fractions Mastery

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  1. Lesson Menu Main Idea and New Vocabulary NGSSS Key Concept: Rational Numbers Example 1: Write a Fraction as a Decimal Example 2: Write a Fraction as a Decimal Example 3: Real-World Example Example 4: Write Decimals as Fractions Example 5: Write Decimals as Fractions Five-Minute Check

  2. Express rational numbers as decimals and decimals as fractions. • rational number • terminating decimal • repeating decimal Main Idea/Vocabulary

  3. Preparation for MA.8.A.6.4Perform operations on real numbers (including integer exponents, radicals, percents, scientific notation, absolute value, rational numbers, and irrational numbers) using multi-step and real world problems. NGSSS

  4. Key Concept

  5. Write as a decimal. means 3 ÷ 16. Write a Fraction as a Decimal 0 .1 8 7 5 Divide 3 by 16. Example 1

  6. Write a Fraction as a Decimal Answer: 0.1875 Example 1

  7. Write as a decimal. A. 0.55 B. 0.5625 C. 0.916 D. 1.7 _ Example 1 CYP

  8. Write as a decimal. can be written as . 3 –33 20 –11 90 –88 2 Write a Fraction as a Decimal Divide 35 by 11 and add a negative sign. Example 2

  9. Write a Fraction as a Decimal Answer: Example 2

  10. Write as a decimal. A. B. C.5.5 D.5.7 Example 2 CYP

  11. 28  54 ENTER 0.5185185185 FRUITWhen Juliana went strawberry picking, 28 of the 54 strawberries she picked weighed less than 2 ounces. To the nearest thousandth, find the fraction of the strawberries that weighed less than 2 ounces. To find the fraction of the strawberries that weighed less than 2 ounces, divide the number of strawberries that weighed less than 2 ounces, 28, by the total number of strawberries, 54. Look at the digit to the right of the thousandths place. Since the digit is 5, round up. Example 3

  12. Answer: The fraction of the strawberries that weighed less than 2 ounces was 0.519. Example 3

  13. SCHOOL In Mrs. Townley’s eighth grade science class, 4 out of 22 students did not turn in their homework. To the nearest thousandth find the fraction of students who did not turn in their homework. A. 0.094 B. 0.148 C. 0.182 D. 0.252 Example 3 CYP

  14. 0.32 0.32 is 32 hundredths. Simplify. Answer: Write a Fraction as a Decimal Write 0.32 as a fraction. Example 4

  15. A. B. C. D. Write 0.65 as a fraction. Example 4 CYP

  16. ALGEBRAWrite as a mixed number in simplest form. Assign a variable to the value . Let N = 2.777... . Then perform operations on N to determine its fractional value. Write Decimals as Fractions Example 5

  17. 25 __ 9 N = Divide each side by 9. Answer: Write Decimals as Fractions N = 2.777... 10(N) = 10(2.777...) Multiply each side by 10 because 1 digit repeats. 10N = 27.777... Multiplying by 10 moves the decimal point 1 place to the right. − N = 2.777...Subtract N = 0.777... to eliminate the repeating part. 9N = 25 Simplify. Example 5

  18. __ Write –0.45 as a fraction in simplest form. A. B. C. D. Example 5 CYP

  19. Write as a decimal. A. 0.785 B. 0.85 C. 0.875 D. 1.142857 ________ Five Minute Check 1

  20. Write as a decimal. A. 0.4 B. 0.416 C. 0.416 D. 2.4 __ _ Five Minute Check 2

  21. Write as a decimal. A. 2.3 B. 2.15 C. 1.15 D. 0.15 Five Minute Check 3

  22. A. B. C. D. Write 0.08 as a fraction in simplest form. Five Minute Check 4

  23. A. B. C. D. Write 1.375 as a mixed number in simplest form. Five Minute Check 5

  24. A. B. C. D. The largest moth is the Atlas moth. The Atlas moth is 11.8 inches long. Which of the following is the length of an Atlas moth written as a mixed number? Five Minute Check 6

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